Note

Reflected Light Phase Curves¶

Citation: Hamill et al. (2024) : Reflected Light Phase Curves with PICASO: A Kepler-7b Case Study

Computing a reflected light phase curve is similar to computing 3D reflected light spectra, but now we will compute reflected spectra for an entire grid of phase angles.

From the previous tutorials you should understand:

How to convert GCM input to PICASO’s required Xarray
How to post-process output to append to GCM ouput
How to run a thermal phase curve and analyze the output

In this tutorial, you will learn:

How to compute a reflected light phase curve
How to analyze the output

[1]:

import pandas as pd
import numpy as np

from astropy import units as u

import xarray as xr

from picaso import justdoit as jdi
from picaso import justplotit as jpi
jpi.output_notebook()

Loading BokehJS ...

Plot the phase curve!¶

[12]:

to_plot = 'fpfs_reflected'
#collapse = [0.40 ]#micron, could select one or more specific wavelengths instead of the mean
collapse='np.mean'

phases, all_curves, all_ws, fig=jpi.phase_curve(allout, to_plot,
                                                collapse=collapse, R=10,reorder_output=True)

jpi.show(fig)

Phase-resolved spectra used to create the phase curve.¶

Since chemistry is randomized for this tutorial and there are no clouds, the spectra is mostly symmetrical across 0 degrees phase angle.

[13]:

#same old same old
wno =[];fpfs=[];legend=[]
for iphase in allout.keys():
    w,f = jdi.mean_regrid(allout[iphase]['wavenumber'],
                               allout[iphase]['fpfs_reflected'], R=100)
    wno+=[w]
    fpfs+=[f*1e6]
    legend +=[str(int(iphase*180/np.pi))]
jpi.show(jpi.spectrum(wno, fpfs, plot_width=500,legend=legend,
                     palette=jpi.pals.viridis(n_phases)))

Calculate cloudy phase curve¶

[17]:

case_3d_clouds.gravity(radius=1,radius_unit=jdi.u.Unit('R_jup'),
                mass=1, mass_unit=jdi.u.Unit('M_jup')) #any astropy units available
case_3d_clouds.star(opacity,5000,0,4.0, radius=1, radius_unit=jdi.u.Unit('R_sun'), semi_major=0.06, semi_major_unit=u.Unit('au'))

allout_clouds = case_3d_clouds.phase_curve(opacity, n_cpu = 3,#jdi.cpu_count(),
                             full_output=False)

[18]:

to_plot = 'fpfs_reflected' #or thermal
#collapse = [0.40 ]#micron
collapse='np.mean'
#phases, all_curves, all_ws, fig=jpi.phase_curve(allout, to_plot, collapse=collapse, R=R)
phases, all_curves, all_ws, fig=jpi.phase_curve(allout, to_plot, collapse=collapse, R=10,plot_width=1500, reorder_output=True)
phases_clouds, all_curves_clouds, all_ws_clouds, fig_clouds=jpi.phase_curve(allout_clouds, to_plot, collapse=collapse, R=10,plot_width=1500, reorder_output=True)
#jpi.show(fig)

Compare cloudy and cloud free¶

Below is a comparison between our cloudless and cloudy phase curves. The cloudy phase curve is much brighter. We also see a shift in the phase maximum due to our inhomogeneous cloud layer.

[19]:

import matplotlib.pyplot as plt

plt.figure(figsize=(15, 7.5))

plt.plot(phases,all_curves * 1e6, label="Cloudless")
plt.plot(phases_clouds,all_curves_clouds * 1e6, label="Cloudy")

plt.xlabel('Orbital Phase')
plt.ylabel('F$_{P}$/F$_{S}$ (ppm)')
plt.title('Reflected Light Phase Curves')
plt.legend(loc='upper left')
plt.rcParams['font.size'] = 15

../_images/notebooks_9g_ReflectedPhaseCurve_33_0.png

Cloudy phase spectra¶

The spectra for phase angles < 180 is flat due to clouds.

[20]:

#same old same old
wno =[];fpfs=[];legend=[]
for iphase in allout_clouds.keys():
    w,f = jdi.mean_regrid(allout_clouds[iphase]['wavenumber'],
                               allout_clouds[iphase]['fpfs_reflected'], R=100)
    wno+=[w]
    fpfs+=[f*1e6]
    legend +=[str(int(iphase*180/np.pi))]
jpi.show(jpi.spectrum(wno, fpfs, plot_width=500,legend=legend,
                     palette=jpi.pals.viridis(n_phases)))

To further analyze your output, you can use all of the same tools found in Modeling a Phase Curve pt 1 (Robbins-Blanch et al. 2022) > Phase Curve Plotting Tools: Phase Snaps

Reflected Light Phase Curves¶

Setting Up Reflected Light Phase Curve¶

Add chemistry.¶

Set up phase curve grid¶

`Atmosphere_4d`¶

Compute the reflected light phase curve.¶

Plot the phase curve!¶

Phase-resolved spectra used to create the phase curve.¶

Reflected phase curve with `Virga` clouds¶

Sanity Check¶

Run clouds_4d¶

Calculate cloudy phase curve¶

Compare cloudy and cloud free¶

Cloudy phase spectra¶

Reflected Light Phase Curves¶

Setting Up Reflected Light Phase Curve¶

Add chemistry.¶

Set up phase curve grid¶

Atmosphere_4d¶

Compute the reflected light phase curve.¶

Plot the phase curve!¶

Phase-resolved spectra used to create the phase curve.¶

Reflected phase curve with Virga clouds¶

Sanity Check¶

Run clouds_4d¶

Calculate cloudy phase curve¶

Compare cloudy and cloud free¶

Cloudy phase spectra¶

`Atmosphere_4d`¶

Reflected phase curve with `Virga` clouds¶